Polymer electrolyte fuel cells have the advantage of being operable in a temperature range around ordinary temperature and are promising for use in a wide variety of fields. In particular, anion-exchange fuel cells do not necessarily require the use of platinum as a catalyst and thus allow cost reduction. Furthermore, anion-exchange fuel cells permit the use of a liquid fuel and can thus be reduced in size. Anion-exchange fuel cells have a separation membrane between an anode and a cathode, and an anion-exchange electrolyte membrane is used as the separation membrane. The anion-exchange electrolyte membrane has a functional group having anion-exchange ability such as a quaternary ammonium group. A method for producing an anion-exchange electrolyte membrane is one in which pores of a microporous polymer base material made of polyolefin resin or the like are filled with an anion-exchange resin which is an electrolyte polymer (see Patent Literature 1, for example).